A question about color
Timaroberts solution will not work because RGB encoded data is relative. That is, for every RGB colour space, the hex values will be different and therefore, without knowing what colour space a hex value is relative to, all degrees of accuracy including floating point representations will be wrong. Never, ever let someone tell you that using a different numerical representation such as hexadecimal or floating point values with many digits of accuracy will solve your colour confusion. No such approach can, and is rooted in misinformation.

This is a simple question to a long and winding path down colour, pixels, and management thereof.

There is also typically no "Blender Representation" but rather different views on the reference data. In this particular instance, the colours in the reference space are scene linear, and the viewport and UI elements may or may not be linearized values depending. There can also be a discrepancy with how OpenGL approximately renders a face versus the actual render.

You are also confusing a display referred imaging application (GIMP) to an application that uses an internally scene referred model (Blender Cycles) which will cause no end of fits for your poor brain.

TL;DR How a colour is stored / encoded as an RGB triplet has different forms and reasons. Within Blender, there are many, many different and diverging views of this reference data which may not align with each other or one's (seemingly reasonable) expectations.

Some answers that might help to illuminate the complex issues at hand:

Colour shift when viewing render outside of blender 
When to use sRGB and when not to?